Question

Let the random variables X & Y have variances 36 and 16 respectively, find the covariance between (X + Y) and (X − Y)

Answer 1

Answer:

         20

Step-by-step explanation:

Need to know:

• cov(aX, Y) = cov(X, aY) = a cov(X, Y)
• cov(X+Y, Z) = cov(X, Z) + cov(Y, Z)
• cov(X, Y) = cov(Y, X)
• cov(X, X) = var(X)

Using these:

cov(X+Y, X-Y)

= cov(X, X-Y) + cov(Y, X-Y)

= cov(X, X) - cov(X, Y) + cov(Y, X) - cov(Y, Y)

= var(X) - cov(X, Y) + cov(X, Y) - var(Y)

= var(X) - var(Y)

= 36 - 16

= 20